My sisters cats would catch things , injure them , then play with them on the patio , flicking them with their paws as they tried to escape . Had the ‘gift’ thing too .Not sure how mice can make a lot of noise ! When we had our house in Tunisia our Birmans cat would regularly hunt at night and then bring us ' live ' presents ' . Gifts included, baby rabbits , lots of voles, birds ( size of thrushes ) and the occasional jerboa. Of course when we heard him meowing with his mouth full we would know he was bring us a gift , then had to get up and try to catch our present as he dropped it on the bed . Luckily as he got to 15 years old his hunting skills deteriorated !